Method and apparatus for improving the vertical resolution of NMR logs

ABSTRACT

An method and system are disclosed for NMR echo-train data acquisition and processing for enhanced vertical resolution for a given signal to noise ratio. In one aspect, the method is based on providing an estimate of non-formation signal components and removing the estimate from the NMR signals. Computation of the estimate is done from the data itself or using a direct measurement of non-formation signals. In another aspect, the functions of reducing coherent noise components is separated from the function of reducing the random noise components, to enhance the resolution of the NMR pulse echo data for a given signal to noise ratio (SNR) of the data. Combination processing is disclosed, which enables efficient filtering of the input NMR data for both relatively high and relatively low SNR of the formation data.

This is a division of application Ser. No. 09/736,754, filed Dec. 14,2000 now U.S. Pat. No. 6,541,969, which claims priority of provisionalapplication 60/170,951, filed Dec. 15, 1999. The content of the aboveapplications is incorporated by reference for all purposes.

FIELD OF THE INVENTION

The present invention concerns nuclear magnetic resonance (NMR) loggingand more specifically relates to a method and apparatus for NMR dataacquisition and processing, which for a given signal-to-noise ratio(SNR) improve the vertical resolution of data logs acquired using NMRlogging tools.

BACKGROUND OF THE INVENTION

In oil and gas exploration it is desirable to understand the structureand properties of the geological formation surrounding a borehole, inorder to determine if the formation contains hydrocarbon resources (oiland/or gas), to estimate the amount and producibility of hydrocarboncontained in the formation, and to evaluate the best options forcompleting the well in production. A significant aid in this evaluationis the use of wireline logging and/or logging-while-drilling (LWD)measurements of the formation surrounding the borehole (referred tocollectively as “logs” or “log measurements”). Typically, one or morelogging tools are lowered into the borehole and the tool readings ormeasurement logs are recorded as the tools traverse the borehole. Thesemeasurement logs are used to infer the desired formation properties.

In recent years nuclear magnetic resonance (NMR) logging has become veryimportant for purposes of formation evaluation and is one of thepreferred methods for determining formation parameters. Improvements inthe NMR logging tools, as well as advances in data analysis andinterpretation allow log analysts to generate detailed reservoirdescription reports, including clay-bound and capillary-bound relatedporosity, estimates of the amounts of bound and free fluids, fluid types(i.e., oil, gas and water), permeability and other properties ofinterest.

NMR tools used in practical applications include, for example, thecentralized MRIL® tool made by NUMAR Corporation, a Halliburton company,and the sidewall CMR tool made by Schlumberger. The MRIL® tool isdescribed, for example, in U.S. Pat. No. 4,710,713 to Taicher et al. andin various other publications including: “Spin Echo Magnetic ResonanceLogging: Porosity and Free Fluid Index Determination,” by Miller,Paltiel, Gillen, Granot and Bouton, SPE 20561, 65th Annual TechnicalConference of the SPE, New Orleans, La., Sep. 23-26, 1990; “Improved LogQuality With a Dual-Frequency Pulsed NMR Tool,” by Chandler, Drack,Miller and Prammer, SPE 28365, 69th Annual Technical Conference of theSPE, New Orleans, La., Sep. 25-28, 1994. Certain details of thestructure and the use of the MRIL® tool, as well as the interpretationof various measurement parameters are also discussed in U.S. Pat. Nos.4,717,876; 4,717,877; 4,717,878; 5,212,447; 5,280,243; 5,309,098;5,412,320; 5,517,115, 5,557,200; 5,696,448 and 5,936,405. The structureand operation of the Schlumberger CMR tool is described, for example, inU.S. Pat. Nos. 4,939,648; 5,055,787 and 5,055,788 and further in “NovelNMR Apparatus for Investigating an External Sample,” by Kleinberg,Sezginer and Griffin, J. Magn. Reson. 97, 466-485, 1992; and “AnImproved NMR Tool Design for Faster Logging,” D. McKeon et al., SPWLA40^(th) Annual Logging Symposium, May-June 1999. The content of theabove patents is hereby expressly incorporated by reference for allpurposes, and all non-patent references are incorporated by referencefor background.

NMR tools of the type discussed above generally measure the time forhydrogen nuclei present in the earth formation to realign their spinaxes, and consequently their bulk magnetization, either with anexternally applied magnetic field, or perpendicularly to the magneticfield, after momentary reorientation due to the application of specificradio frequency (RF) pulses. The externally applied magnetic field istypically provided by a magnet disposed in the tool. The spin axes ofthe hydrogen nuclei in the earth formation are, in the aggregate, causedto be aligned with the magnetic field induced in the earth formation bythe magnet. The NMR tool includes an antenna positioned near the magnetand shaped so that a pulse of radio frequency (RF) power conductedthrough the antenna induces a magnetic field in the earth formationorthogonal to the field induced by the magnet. The RF pulse has aduration predetermined so that the spin axes of the hydrogen nucleigenerally align themselves perpendicular both to the orthogonal magneticfield induced by the RF pulse and to the externally applied magneticfield. After the pulse ends, the nuclear magnetic moment of the hydrogennuclei gradually relax, i.e., return to their alignment with theexternally applied magnetic field; at the same time an antenna, which istypically the same as the one used by the initial pulse, is electricallyconnected to a receiver, which detects and measures voltages induced inthe antenna by precessional rotation of the spin axes of the hydrogennuclei.

An actual NMR measurement involves a plurality of pulses grouped intopulse sequences, most frequently of the type known in the art asCarr-Purcell-Meiboom-Gill (CMPG) pulsed spin echo sequences. As known inthe art, each CPMG sequence consists of a 90-degree (i.e., π/2) pulsefollowed by a large number of 180-degree (i.e., π) pulses. The 90-degreepulse rotates the proton spins into the transverse plane and the180-degree pulses generate a sequence of spin echoes by refocusing thetransverse magnetization after each spin echo.

It should be apparent that it is important for the NMR measurements toregister only signals that are generated by the formation of interest.However, non-formation signals—often referred to as “offset” or“ringing” signals—arise for a variety of reasons. For example, they maybe caused by the high-sensitivity tool electronics (e.g., “offsets”), ormay be due to magnetostrictive effects (e.g., “ringing”) that arise frominteractions between pulsed magnetic fields and electronic or magneticcomponents in the tool. For example, when RF pulses are applied to theantenna, the magnet can become physically deformed by magnetostriction.After each RF pulse is turned off, the magnet tends to return to itsoriginal shape in a series of damped mechanical oscillations, known as“ringing.” Ringing induces voltages in the antenna, which can interferewith measurement of the voltages induced by the spin echoes.

A method known in the art for reducing the effect of offsets, ringingand possibly other non-formation signals is to make spin echomeasurements in predetermined cycles. Typically, two pulse sequences ofopposite phase are acquired to cancel electronic offsets and 180-degreeringing. The pair of pulse sequences is called a phase-alternated pair(PAP). PAP measurements are performed by making a second set of spinecho measurements starting with an original transverse alignment (90degree) RF pulse, which is inverted in phase from the 90 degree pulseused to start the first set of spin echo measurements. Voltages inducedin the antenna during the second set of spin echo measurements areinverted in polarity from the voltages induced in the first set ofmeasurements. The signals from the second set of measurements can thenbe subtracted from the signals in the first set of measurements tosubstantially remove coherent noise, such as the ringing-inducedsignals. (For simplicity, in the following discussion “ringing” will beused as a catch-all term designating undesirable non-formation signals).Accordingly, in the “PAP method” successive echo-train signals areacquired from the formation that are alternately in-phase and anti-phasewith respect to signals that are generated outside the formation; thus,a typical PAP simply comprises any adjacent pair of in-phase andanti-phase CPMG echo-trains. An implicit assumption in this operation isthat the tool-related, non-formation signals in an echo-train cansomehow be characterized, and that they change little, or even not atall, between successive echo-trains.

Mathematically, the PAP method can be illustrated as follows. Supposethat an individual spin echo train (CPMG₀) can be characterized as asummation of a decaying NMR signal from the formation (S₀), anon-formation signal (O₀), and random or thermal noise (n₀), so thatCPMG₀=S₀+O₀+n₀. The subsequent phase-alternated echo-train (CPMG₁), isthen given by CPMG₁=−S₁+O₁+n₁. Since changes in the non-formation signalare assumed to be minimal, the difference between the two echo-trains(PAP) cancels the non-formation signals, leaving an echo-train that is acomposite of the signals and the noise, i.e.:PAP=(S ₀ +S ₁)+n _(Δ).

Accordingly, in the prior art non-formation noise is removed using theabove PAP process, in which one or more phase alternate pair signals aresubtracted to remove the ringing. The two acquisition sequences in eachphase alternate pairs must be separated in time by T_(W), the time torepolarize the media. During logging, the tool is moving at a speed v,so that the PAPs are separated by a distance equal to v*T_(W). Clearly,this limits the vertical resolution achievable with the tool.

It is thus apparent that to minimize or ideally eliminate non-formationcomponents of the input signal, in accordance with the prior art it isthe PAP, rather than the individual echo-train that becomes the basicmeasured element, which is then processed in similar manner to NMRecho-trains acquired in a laboratory. A potential advantage of the priorart method is that it results in increased SNR of the output signal dueto the averaging operation. As discussed above, however, using PAPs asopposed to single echo trains as basic measurement units also introducesa delay that places various constraints on both the achievable loggingspeed and the vertical resolution of NMR logs.

As noted, prior art methods use a single operation to accomplish boththe ringing elimination, as well as the signal-to-noise improvement bymeans of experiment stacking. One requirement of the prior art methodsis to select an amount of stacking necessary for a desired SNR thatincludes, with equal weight, every PAP at every acquired frequency. Thisis typically referred to as “boxcar” filtering of the data. For an NMRtool operating at a single frequency, the number of PAPs stacked issimply one or more. For NMR logging tools, such as the MRIL Prime,operating at N frequencies, the numbers of PAPs stacked must be amultiple of N. Since each PAP comprises two echo-trains, the minimumstacking for the MRIL tool is two times the number of acquiredfrequencies. There are two problems associated with this approach.First, in formations with high signal-levels, the approach results inmore stacking than is necessary to provide adequate signal-to-noiseratio. On the other hand, for those formations with lower signal-levels,in which more stacking is required to obtain adequate SNR, it isnecessary to select an amount of stacking, which is a multiple of theminimum stacking. This is undesirable at least because the extraaveraging introduces undesirable processing delays and, as shown below,reduces the maximum vertical resolution.

As shown in the detailed disclosure, in accordance with the presentinvention an alternative approach can be used where the ringing andrandom noise components are processed in two steps with possiblydifferent filters. The results show that the (vertical) resolution ofNMR logs can be improved in many cases. The output of the proposedprocessing method is consistently less noisy and more robust even inthose cases where there is not a significant vertical resolutionimprovement compared to the conventional boxcar filter approach.

Focusing next on another deficiency associated with the prior art, as aconsequence of the PAP method, the “best-possible” effective verticalresolution of an NMR log acquired with a moving tool is a combination ofboth the inherent vertical resolution of the tool antenna—the antennaaperture—and the distance traveled between the pair of echo-trainmeasurements that comprise a PAP. As discussed above, however, in manylogging situations the vertical resolution is further compromised by theneed to average data from multiple PAPs to ensure an adequatesignal-to-noise ratio (SNR) for confident data analysis. For example, itis known in the art to improve the SNR of NMR well logging measurementsby averaging a plurality of PAPs, typically eight or more.

Depending on the specific “PAP accounting method” employed, echo-trainscan form PAPs in a number of different ways. For example, in one method,two adjacent echo-trains form a single PAP, three adjacent echo-trainsform two PAPs, and four echo-trains form three PAPs. In an alternativemethod, while two adjacent echo-trains still form a single PAP, fouradjacent echo-trains might be needed to form two PAPs, with six adjacentecho-trains needed to form three. See FIG. 11A. Illustrated in thefigure is the “overlapping” mode of operation (of the CMR tool discussedabove), where one PAP is acquired every sample interval. As illustrated,in an overlapping mode the two CPMGs overlap half of the sampleinterval, and the tool relies on the wait time to polarize the hydrogenspins for the NMR measurement. The logging speed (v) of the tool dependson a number of factors, primarily the sample interval and themeasurement wait time.

As shown in FIG. 11B in a different embodiment of the CMR tool (CMRPlus), to speed up the measurements the tool uses a new measurementsequence called a sequential PAP. As illustrated, the tool acquires asingle CPMG per sample interval, and the phase of each successive CPMGis shifted 180 degrees. A PAP is formed every sample interval bycombining the most recent CPMG with the prior CPMG. This measurementsequence allows the tool to move faster, however, it is apparent thatthe number of independent CPMGs is reduced, which increases the noiselevel.

In earlier models of the MRIL tool, the typical logging speed used toacquire NMR data is sufficiently low, so that the effective verticalresolution of the NMR log is dominated by the need to stack multiplePAPs to obtain adequate SNR. For the multi-frequency MRIL Prime tool,however, the use of multiple NMR measurement frequencies is conceptuallyequivalent to the simultaneous acquisition of multiple passes with theearlier logging tools. Thus, MRIL Prime logs could be acquired at fasterlogging speeds, with the required SNR obtained by stacking multiple PAPsacross the frequency bands.

Unfortunately, in high-signal formations (e.g., high porosity, oil-orwater-filled rocks), where the logging speeds can be comparatively fast,the effective vertical resolution of the NMR log becomes dominated bythe tool movement during a single PAP. For example, with a recovery timeof 10 seconds between echo-trains in a PAP, with PAPs acquired at allpossible frequencies, the elapsed time between the first echo-train inthe first-frequency PAP and the second echo-train for the last-frequencyPAP, is close to 20 seconds. At a logging speed of 900 ft/hr (15ft/min), the MRIL tool will move approximately 5 feet during thismeasurement: when combined with the inherent vertical resolution of theantenna (which is approximately 2 feet), the effective verticalresolution becomes roughly 7 feet.

Enhancing the resolution of the logs is a significant problem, becausesubsurface formations are generally heterogeneous, so that porosity,saturation and lithology vary with position. A common example ofheterogeneity is the presence in the formation of geological layers, orbeds. Because logging tools have a nonzero volume of investigation, morethan one layer may lie within the volume of investigation of a tool. Insuch cases, the petrophysical evaluation of one layer may be distortedby the presence of another layer falling within the larger volume ofinvestigation of the tool. The above phenomenon leads to a specificproblem in the analysis of subsurface formations that include one ormore underground layers, especially when the layers are thin comparedwith the vertical resolution of the measuring tool. Such layers havebecome subject to significant commercial interest because of theirproduction potential. Any knowledge about the composition and propertiesof such layered formations that helps better estimate their productionpotential has thus become increasingly valuable.

Clearly, to make the best use of the NMR logging tools, it is necessarythat the current reliance on the PAP as the basic measured element bereduced. Clearly, if for example the MRIL Prime data can be acquiredand/or processed in such a manner that a single echo-train, rather thana PAP, becomes the basic unit of measurement, then it becomes possibleto provide an NMR log with an effective vertical resolution much closerto the inherent resolution defined by the length of the tool antenna.Using the assumptions in the example above, if it was only necessary tostack echo-trains from four frequencies to obtain adequate SNR, theelapsed time of the measurements would be about 5 seconds, during whichtime the MRIL tool would move approximately 1 foot, resulting in theeffective vertical resolution of the NMR log of approximately 3 feet. Itis clear therefore that any mechanism that for a given SNR supported bythe formation can increase the vertical resolution of the tool withoutdecreasing the logging speed is highly desirable.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to overcomedeficiencies associated with the prior art and in particular to providea method and system for improving the resolution of borehole NMR loggingmeasurements and for suppressing artifacts in NMR data obtained fromlogging measurements.

These and other objects are accomplished in accordance with a preferredembodiment of the present invention by a novel approach in whichnon-formation. i.e., ringing, signals are characterized and removed fromthe underlying NMR spin echo signals in separate steps. In particular,to analyze the ringing signal it is first proposed to combine two ormore acquisition sequences in such a manner as to obtain an estimate ofthe ringing component of the signal, which is assumed to be a constantor a slowly varying function. In the following step of the process,various signal processing or statistical methods are applied to removethe estimated ringing component from the acquisition sequence. In asecond embodiment, the ringing component of the signal is estimated bydirect measurement using a separate NMR pulse sequence, which in aspecific implementation is a standard CPMG pulse echo sequence withoutthe leading 90 degree pulse. Such sequence will generally containringing but not any decay signals, i.e., formation signals. Once theringing constant (or slowly varying function) is established, it isremoved from the NMR acquisition data. In both embodiments, experimentstacking is performed as known in the art to increase the signal tonoise ratio of the signal. In a preferred embodiment, the steps ofringing estimation and removal and the step of experimental stacking canbe performed as a single pass through the acquired data, CPMG by CPMG,typically in a successive or chronological fashion. Alternatively, themethod can have the first two steps performed in a single pass throughthe acquired data in a successive fashion, with the third step performedas a second pass. Following these steps, the NMR signal is processed asknown in the art to obtain parameters of interest characterizing theformation.

In particular, according to this invention a system and method areproposed for the interpretation of NMR echo-train data. In one aspect,the invention is a method for determining properties of geologicformations using nuclear magnetic resonance (NMR) logging, comprising:providing a plurality of phase alternated NMR pulse echo trains from ageologic formation; estimating non-formation signal contribution in theplurality of NMR pulse echo trains; removing the estimated non-formationsignal contribution from at least some of the plurality of NMR pulseecho trains; and determining properties of the geologic formation basedat least in part on NMR pulse echo trains in which the estimatednon-formation signal contribution had been removed. In a preferredembodiment, the NMR pulse echo trains are Carr-Purcell-Meiboom-Gill(CMPG) spin echo trains. Further, non-formation signal contribution isestimated from two or more of the plurality of CPMG spin echo trains,preferably using one or more phase-alternated pair(s) (PAPs) of CPMGspin echo trains. In a specific implementation two PAPs are used thatare formed by a current CPMG spin echo train (CPMG₀) and an immediatelypreceding (CPMG⁻¹) and an immediately following (CPMG₊₁) phasealternated CPMG spin echo trains.

In another embodiment, non-formation signal contribution is estimatedusing a separate NMR pulse echo train, which preferably is a CPMG spinecho train without an initial π/2 pulse.

In another aspect, the invention is a method for increasing theresolution of NMR log data obtained using a multi-frequency NMR toolhaving N operating frequencies, comprising: (a) providing a NMR pulseecho signal comprising components corresponding to at least two of the Noperating frequencies of the tool; (b) separating the provided pulseecho signal into two or more data-flow paths, each data flow pathcorresponding to an operating frequency of the tool; (c) filtering thesignal in each separate data flow path using a first filter designed toreduce the contribution of non-formation signal components; and (d)filtering the output signal from the first filter to achieve apredetermined signal-to-noise ratio (SNR) for a given resolution of theNMR log data. In a preferred embodiment, step (d) is performed using atapered filter, which may be a Hamming filter. In a preferredembodiment, the first filtering operation in step (c) is performed onphase alternated pairs (PAPs) of signals.

In yet another aspect, the invention is a system for increasing theresolution of NMR log data obtained using a multi-frequency NMR toolhaving N operating frequencies, comprising: means for providing a NMRpulse echo signal comprising components corresponding to at least two ofthe N operating frequencies of the tool; means for separating theprovided pulse echo signal into two or more data-flow paths, each dataflow path corresponding to an operating frequency of the tool; means forfiltering the signal in each separate data flow path using a firstfilter designed to reduce the contribution of non-formation signalcomponents; and means for filtering the output signal from the firstfilter to achieve a predetermined signal-to-noise ratio (SNR) for agiven resolution of the NMR log data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a NMR logging system used in accordancewith the present invention;

FIG. 2 is a partially schematic, partially block diagram of a NMRlogging tool and attached electronics used in a preferred embodiment;

FIG. 3 is an illustration of a standard CPMG sequence along with aringing estimation pulse sequence (REPS) used in a direct measurement ofringing signal contribution in accordance with a specific embodiment ofthis invention;

FIGS. 4 a, 4 b, 4 c, 4 d, 4 e and 4 f illustrate intermediate resultsfor the Ringing Estimation step and results after Ringing Eliminationstep (step 2) used in a preferred embodiment of this invention;

FIG. 5 illustrates the effects of different levels of experimentstacking as applied in the Experiment Stacking step in accordance withthe present invention;

FIGS. 6 through 10 illustrate how different amounts of experimentstacking impact the vertical resolution of a section of log data inaccordance with the present invention;

FIGS. 11A and 11B illustrate overlapping phase alternated pairs (PAPs)and sequential PAPs;

FIG. 12 illustrates the frequency response of several boxcar filters,which are used in the prior art methods;

FIGS. 13A, 13B and 13C are plots of the filter coefficients of thebox-car (A), Comb filter (B), and a Hamming filter (C);

FIGS. 14 through 18 illustrate comparisons between the frequencyresponse of box car filters used in the prior art with combinationfilters used in accordance with the present invention;

FIG. 19 illustrates the application of four filters, to a 1995-vintage,dual-frequency MRIL-C log;

FIGS. 20 and 21 show a comparison of standard processing, versus themethod of this invention, in a Baker-Atlas well, MRIL-C log, 6 and 3second wait time, respectively;

FIGS. 22, 23 and 24 illustrate in more detail the method of the presentinvention replacing standard box-car processing with a two-stagefiltering.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

I. The System

FIG. 1 is a block diagram of a system in accordance with a specificembodiment of the present invention, which shows individual blockcomponents for controlling data collection, processing of the collecteddata and displaying the measurement results. In FIG. 1 a logging tool106 comprises an NMR probe controller 30 and pulse echo detectionelectronics and is lowered in a borehole drilled in the formation 109.The output signal from the tool detection electronics is processed bydata processor 12 to record NMR pulse echo data from the tool andanalyze the relaxation characteristics of the materials surrounding theborehole. The output of the data processor 12 is fed to parameterestimator 40. Measurement cycle controller 22 provides an appropriatecontrol signals to the probe. The processed data from the logmeasurements is stored in data storage 60. Data processor 12 isconnected to display 50, which is capable of providing a graphicaldisplay of one or more measurement parameters, preferably superimposedon display data from data storage 60. The components of the system ofthe present invention shown in FIG. 1 can be implemented in hardware orsoftware, or any combination thereof suitable for practical purposes.

Reference is now made to FIG. 2, which illustrates in a semi-blockdiagram form an NMR logging apparatus, such as the MRIL Prime tool ofNumar Corporation (a Halliburton Company), which can be used for NMRmeasurements in accordance with the present invention. In standardoperation, first portion 6 of the tool is arranged to be lowered into aborehole 7 having a borehole longitudinal axis 8 in order to examineproperties of the geologic formation in the vicinity of borehole 7.

The first portion comprises a generally cylindrical permanent magnet 10,preferably having a longitudinal axis 11, which is preferably coaxialwith the longitudinal axis 8 of the borehole. Alternatively, a pluralityof permanent magnets 10 may be employed. Permanent magnet 10 preferablyhas uniform magnetization substantially perpendicular to thelongitudinal axis of the logging tool, which is parallel to thelongitudinal axis 8 of the borehole 7.

The first portion 6 also comprises one or more coil windings 16, whichpreferably are arranged on top of the permanent magnet and form the toolantenna. The magnetization direction 13 created by the antenna issubstantially perpendicular to the longitudinal axis 8 of the bore hole.The coil winding 16, together with a transmitter/receiver (T/R) matchingcircuit 20 define a transmitter/receiver (T/R) circuit. T/R matchingcircuit 20 typically includes a resonance capacitor, a T/R switch andboth to-transmitter and to-receiver matching circuitry and is coupled toa first RF power amplifier 24 and to receiver preamplifier 26.

The permanent magnet 10 and coil windings 16 are preferably housed in anon-conductive, non-ferromagnetic protective housing 18. The housing andits contents will hereinafter be referred to as the probe 19.

In operation, the probe along with RF amplifier 24, preamplifier 26 andT/R matching circuit 20, designated collectively as housing 28 arepassed through the borehole. Alternatively, some of the above elementsmay be located above ground in housing 30.

Disposed in a housing indicated in FIG. 2 by block 30, is a controlcircuitry, including a computer 32, which provides a control output to apulse programmer 34. Pulse programmer 34 controls the operation of phaseshifter 44, as well as an RF driver 38, which drives RF power amplifier24. Pulse programmer 34 controls the operation of a variable frequencyRE source 36, the output of which is passed through phase shifter 44 tothe RF driver 38. The signal from RE driver 38 is amplified in RE poweramplifier 24 and passed through T/R matching circuit 20 to the coilwinding 16.

NMR signals from excited nuclei in the formation surrounding theborehole are picked up by the receiving antenna 16 and passed throughT/R matching circuit 20 to RF receiver pre-amplifier 26, the output ofwhich is supplied to an RF receiver 40 which also receives an input fromphase shifter 44. Receiver 40 outputs via an A/D converter with a buffer46 to the computer 32 for providing desired well logging output data forfurther use and analysis.

Further details of the construction and operation of the tool used inaccordance with a preferred embodiment of the present invention can befound in U.S. Pat. Nos. 4,710,713 4,717,876; 4,717,877; 4,717,878;5,212,447; 5,280,243; 5,309,098; 5,412,320; 5,517,115, 5,557,200 and5,696,448. The content of the above patents is hereby expresslyincorporated by reference. It will be appreciated that while the MRILtool is used in a preferred embodiment, any other tool notably the CMRand CMR-Plus tools by Schlumberger, or other available tools, such asthose by Baker-Atlas and Computalog, as well as logging-while-drilling(LWD) tools, appropriately programmed, can also be used in alternativeembodiments.

II. The Methods

In accordance with one aspect of the present invention, a novel approachis proposed for reducing the level of non-formation signals, i.e.,ringing, in which ringing signals are characterized and removed from theunderlying NMR pulse echo signals in separate steps. Once the estimatedringing component is removed from the acquisition sequence(s), inaccordance with one embodiment of the invention, standard NMR processingmethods are applied to derive petrophysical properties of the formationbeing investigated. In accordance with another aspect of the invention,which is described in Section D below, additional pre-processing isapplied to the signal to further improve the resolution of the tool.

First is considered a method for reducing the level of ringing in thesignal for a given signal-to-noise ration (SNR) using a multi-stepapproach. In a preferred embodiment, there are three conceptual steps,broadly designated: Ringing Estimation; Ringing Elimination; andExperiment Stacking.

A. Ringing Estimation

In a preferred embodiment of the invention, an estimated ringing levelfor each measurement is obtained in the Ringing Estimation step throughuse of a three-operation process. The three operations include: (a)providing a Basic Ringing Estimate; (b) providing an Echo Time Average;and (c) computing a PAP Mean Ringing Average.

A.1. Basic Ringing Estimate

In accordance with the present invention, two methods are proposed fordetermining the Basic Ringing Estimate. In a first, preferred method,computing the Basic Ringing Estimate is a data-driven determination fromthe echo-trains that comprise the phase-alternated pairs (PAPs). Inaccordance with an alternative embodiment, the Basic Ringing Estimate iscomputed using a direct measurement (DM) of the ringing from a special“ringing echo-train” acquired immediately before or after a normalecho-train.

A1.a. Basic Ringing Estimate [PAP]

The Basic Ringing Estimate [PAP] operation in accordance with thepreferred embodiment comprises summing the current measurement CPMG spinecho train with one of more of the current measurement's PAP CPMG echotrains. This operation is performed on an echo by echo basis for eachPhase Alternate Pair separately, which results in one or more basicringing estimate vectors, the length of which is determined by thelength of the echo trains.

In particular, in a preferred embodiment the method uses the currentmeasurement CPMG (denoted CPMG₀—which is a vector having N elements,where N is the length of the spin-echo sequence) with the two nearestCPMG echo trains, with which it forms PAPs, i.e., the “preceding”alternate phase echo train (CPMG⁻¹) and the “following” alternate phaseecho train (CPMG₊₁)—to create two estimates of the basic ringingestimate vectors, each having N elements. Mathematically, the basicringing estimates can be expressed as follows: $\begin{matrix}\begin{matrix}{{{Ringing}_{- 1}(n)} = \frac{{{CPMG}_{0}(n)} + {{CPMG}_{- 1}(n)}}{2}} \\{{{Ringing}_{+ 1}(n)} = \frac{{{CPMG}_{0}(n)} + {{CPMG}_{+ 1}(n)}}{2}}\end{matrix} & {{Eqn}.\quad(1)}\end{matrix}$

Because the CPMG echo trains are acquired in quadrature, it will beappreciated that the operations described above, and in subsequentequations, are performed in the complex domain, i.e., by treatingseparately the real and imaginary signal input channels.

Assuming that the CPMG echo-trains acquired at a single frequency can berepresented by the following sequence relative to some arbitrarystarting sample at 0:. . .−S⁻³+OS⁻²+O−S⁻¹+OS₀+O−S₊₁+OS₊₂+O−S₊₃+O. . .where S₀ is the formation signal at depth 0, O is the tool-generatednon-formation signal, and the signs are arranged such that each adjacentpair is a PAP. In the notation used above, CPMG₀ is equal to S₀+O, andnecessarily contains random or thermal noise that arises in both theformation and non-formation signals. The random noise component isomitted for convenience.

Using Eqn. (1), the 2 PAPs incorporating (S₀+O) are summed in such amanner that they yield (in vector notations):$\left( {\frac{\left( {{\overset{\_}{S}}_{0} - {\overset{\_}{S}}_{- 1}} \right) + {2\overset{\_}{O}}}{2} + \frac{\left( {{\overset{\_}{S}}_{0} - {\overset{\_}{S}}_{+ 1}} \right) + {2\overset{\_}{O}}}{2}} \right)/2$where the bar superscript denotes the Echo Time Averaging described inmore detail below.

The expression above, which describes the MeanRingingAverage from thethird processing step can then be simplified to:$\overset{\_}{O} + \frac{{2{\overset{\_}{S}}_{0}} - \left( {{\overset{\_}{S}}_{- 1} + {\overset{\_}{S}}_{+ 1}} \right)}{4}$

As can be seen, the MeanRingingAverage includes some information aboutthe formation. Specifically, it carries information about the change information signal—as represented by {overscore (S)}—over a depth intervalcomprising two PAPs. If {overscore (S)} varies linearly with depth overthe scale of two adjacent PAPs—three adjacent echo-trains at the samefrequency—then the formation signal present in the MeanRingingAveragecancels out and the only component remaining is the non-formationsignal, Ō.

As an example of a practical case in which the formation signaldisappears from the MeanRingingAverage, consider the situation at theboundary between two “thick” beds; where “thick” in this case meanshaving a thickness greater than the antenna aperture of the tool. IfCPMG⁻¹ and CPMG₊₁ are measured one antenna aperture apart and straddlingthe boundary, then CPMG₀ will be the mean of the CPMG echo-trains aboveand below: In this case, {overscore (S)} will vary linearly with depthand MeanRingingAverage will be given simply by Ō. It should be notedthat, in the preferred embodiment described above, the non-formationsignal is assumed to be constant, having a value which may be a complexnumber.

While the preferred method described above uses two PAPs, it will beappreciated that there is no implied limitation on the maximum number ofPAPs that could be used. Similarly, while the preferred method createstwo Ringing Estimates, there is no implied limitation as to this number,since a single Ringing Estimate could be computed from a single PAP andcan be used for the subsequent operations instead. It should also beapparent that more than two estimates can be formed at this time inalternative embodiments.

A1.b. Basic Ringing Estimate [DM]

In accordance with the direct measurement embodiment of the presentinvention, a Ringing Estimation Pulse Sequence (REPS) is used todetermine directly the Basic Ringing Estimate. The Basic RingingEstimate [DM] simply makes a separate measurement with a CPMG pulsesequence specifically designed to produce the ringing signal alone(designated as RING₀) without any other external or formation signal. Inthis case, Ringing₀, which is the ringing signal associated with thecurrent sequence CMPG₀, is directly obtained from the CPMG sequence,using the expression:Ringing₀(n)=RING₀(n)  Eqn.(2)

In a preferred embodiment, the REPS sequence that can be used is a CPMGsequence without an initial π/2 pulse. It will be appreciated by thoseskilled in the art that such sequence will create an echo-train thatcontains no formation signal, but which contains the needed informationto characterize the non-formation signals.

Accordingly, in a preferred embodiment the REPS is a short sequence (10to 30 echoes) of π pulses. The sequence is substantially identical tothe CPMG sequence used in the standard measurement, except that itcontains fewer 180 degree (i.e., π) pulses and no 90 degree pulse. Thatis, the REPS sequence should be a string of π pulses with the sameseparation as in the following (or preceding) CPMG measurement sequenceand the same pulse shape. Preferably, the sequence is run for everyfrequency used in the operation of the multi-frequency tool. Generally,REPS is run during the wait time between CPMG measurement sequences. Theexact location depends on the activation being run as it depends on toolpower/energy being available.

The REPS used in this embodiment of the invention is illustrated in FIG.3. As shown, in the a timing diagram that illustrates an embodiment of astandard “CPMG Measurement Sequence”—presumably acquired after somebuild-up time T_(W)—followed by a “Ringing Estimation Sequence” . Alsoshown in the drawings are the windows at which spin-echoes are acquiredan interval T_(E)/2 after the π-pulses. As noted above, in the RingingEstimation sequence, the measurements made in the spin-echo windows willactually be of the ringing signal and not of the formation spin-echoes.

The preferred embodiment shows the Ringing Estimation Sequence followingthe CPMG Measurement Sequence, with the first π-pulse occurring aninterval T_(E) after the last spin-echo window in the CPMG MeasurementSequence. The Ringing Estimation Sequence differs from the CPMGMeasurement Sequence in that the first π/2-pulse is omitted, and in thatthe number of echoes in the Ringing Estimation Sequence (Nr) is notnecessarily the same as the number of echoes in the CPMG MeasurementSequence (N). N and Nr are set according to the need to characterizeseparately the formation signal (N) and the ringing signal (Nr). It willbe appreciated that in alternative embodiments of the invention thedirect measurement sequence may precede the CPMG measurement sequence.

A.2. Echo Time Average

In accordance with the present invention, the Echo Time Averageoperation provides one or more mean ringing estimates. Broadly, theoperation comprises calculating the average value of the basic ringingestimate vectors determined in the Basic Ringing Estimate operationdescribed in Section A.1. above. In particular, in accordance with apreferred embodiment, the computation is mathematically expressed asfollows: $\begin{matrix}\begin{matrix}{{MeanRinging}_{- 1} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\quad{{Ringing}_{- 1}(n)}}}} \\{{MeanRinging}_{+ 1} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\quad{{Ringing}_{+ 1}(n)}}}}\end{matrix} & {{Eqn}.\quad(3)}\end{matrix}$

In the event that the Basic Ringing Estimate [DM] method has been used,then only one summation is needed: $\begin{matrix}{{MeanRinging}_{0} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\quad{{Ringing}_{0}(n)}}}} & {{Eqn}.\quad(4)}\end{matrix}$

In the preferred embodiment expressed mathematically in Eqn. (3) and(4), all of the basic ringing estimate vector elements being used forcalculating the average values are computed, yielding a single possiblycomplex number, which is an estimate of the contribution ofnon-formation, i.e., ringing signals. In the most general case it isunlikely that ringing will remain constant over the course of the NMRmeasurement or even over the course of a sequence. Accordingly, inalternative embodiments of this invention one or more subsets of thevector elements could be used instead, thereby generating a slowlydeveloping complex function, which may be expected to more closelyestimate the ringing phenomenon. It will be appreciated that if morethan one subset is used, then MeanRinging will be cast as acomplex-vector.

A.3. PAP Mean Ringing Average

In a preferred embodiment, the PAP Mean Ringing Average operationconsists of combining one or more of the mean ringing estimatesdetermined in the Echo Time Average Operation. This operation calculatesthe final estimated ringing level by calculating the mean of theseparate mean ringing estimates, expressed mathematically as follows:$\begin{matrix}{{MeanRingingAverage} = \frac{{MeanRinging}_{+ 1} + {MeanRinging}_{- 1}}{2}} & {{Eqn}.\quad(5)}\end{matrix}$

In the event that the Basic Ringing Estimate [DM] method has been used,then MeanRingingAverage is identical to MeanRinging₀. In the event thatMeanRinging is a complex-vector, then the method for computingMeanRingingAverage results in a complex-valued vector.

In accordance with the present invention, it has been found that theassumption of a constant ringing signal is more closely matched if thefollowing condition is met:T _(E) *f=Ni.e., when the product of the echo spacing (T_(E)) in milli seconds andthe operating frequency (f) for the CPMG spin echo train(s) is aninteger number N.

In addition to the preferred method(s) described above, otheralternative methods for performing the Ringing Estimation step can beused and include, but are not limited to:

-   -   (a) Using just a single PAP that incorporates the current        primary CPMG;    -   (b) Using more than single Phase Alternate Pair CPMGs both        preceding and following the current primary CPMG;    -   (c) Using one or more PAPs or other combinations of echo-trains        that may or may not incorporate the primary current CPMG;    -   (d) Making intermediate ringing level estimates and then using        other filters, or means of characterization, to determine the        final estimated ringing level;    -   (e) Making intermediate ringing level estimates and then        characterizing any depth-dependent behavior of the ringing level        estimates to determine the final estimated ringing level.

Using the principles of this invention outlined above, computation ofthe Ringing Estimates using the above alternative methods can be derivedby persons of average skill in the art, and will not be considered infurther detail. Other methods or variations of the Ringing Estimateprocessing step will be apparent to those skilled in the art and areintended to be used, where applicable.

B. Ringing Elimination

In accordance with the present invention, the estimated level of ringing(a single number or slowly varying function) obtained in the previousstep and described in Section A above is next removed in the step ofRinging Elimination from the current CPMG echo-train measurement. Thisringing elimination is accomplished in accordance with a preferredembodiment by subtracting the estimated ringing from each and every echoof the current measurement CPMG echo train, as expressed below:CPMG′₀(n)=CPMG₀(n)−MeanRingingAverage  Eqn.(6)

Again, since the CPMG echo train and the estimated ringing have both areal and imaginary component, the ringing elimination is performed forboth the real and imaginary channels.

C. Experiment Stacking

Experiment stacking is used in accordance with the present invention inorder to improve the signal-to-noise ratio (SNR) to an adequate level.It should be noted that for multi-frequency tools, such as the MRILPrime tool, this step means that the experiment stacking is performedacross one or more frequencies depending on how the data was acquired.

Experiment stacking is employed in accordance with the present inventionin two embodiments. In a first embodiment, the method uses a boxcarrunning average filter, whose length depends primarily on the desiredsignal-to-noise. It will be appreciated by those of skill in the art,that using filters with no other length constraints is a distinctimprovement over the prior art, where the filter length is calculated asa multiple of the number of frequencies and phase alternate pairs(PAPs). Therefore, where the data dictates it, in accordance with thepresent invention on can use a boxcar filter of length 10, whereas inprior art stacking one would have to use a filter of length 16, whichintroduces processing delays and may lead to decreased verticalresolution of the data.

In a preferred second embodiment, instead of using a boxcar filter forthe Experiment Stacking step other types of filters can be usedadvantageously and may be more appropriate for achieving the desiredsignal-to-noise ratio. For example, the filters described below inSection D provide an alternative to boxcar filtering to improve thevertical resolution of NMR logs such as those obtained by the MRIL tool.

In accordance with a preferred embodiment, all three steps discussed inSections A, B and C above can be performed as a single pass through theacquired data, CPMG by CPMG, typically in a successive or chronologicalfashion. In an alternative embodiment, the first two steps can beperformed in a single pass through the acquired data in a successivefashion, with the third step performed as a second pass.

Post-Processing

After Experiment Stacking, which in accordance with this invention isthe last pre-processing step, stacked CPMG echo trains can be treated inthe same fashion as the stacked CPMG echo trains that result from priorart methods: for example, the stacked echo-trains could be“phase-rotated”, and then “inverted in the T₂ domain” to obtain the “T₂spectrum” of the echoes, as known in the art. The interested reader isdirected to the disclosure of U.S. Pat. No. 5,517,115, as well as U.S.Pat. Nos. 5,212,447; 5,280,243; 5,309,098; 5,412,320; 5,557,200 and5,696,448 for a detailed description of these methods.

Proposed Method: Special Case

The proposed method can, optionally, be altered in those circumstancesin which the Experiment Stacking requires stacking echo-trains acrossPAPs. In this case, the Ringing Estimation and Ringing Elimination stepscan be accomplished by taking the PAP differences—as is done in thecurrent method—and then applying the appropriate type of ExperimentStacking. This approach is further addressed in Section D below.

EXAMPLES

FIG. 4 shows graphically the results of the first and second processingsteps discussed above. For all plots, the x-axis is the echo time andthe y-axis is the echo or ringing amplitude, the real channel echoamplitudes are shown in red and the imaginary channel amplitudes areshown in green. (color drawings attached, as well as black and white).

FIGS. 4 a-4 c show the input primary phase CPMG echo train (CPMG₀) inFIG. 4 b. The input alternate phase CPMG echo train following theprimary phase (CPMG₊₁) is shown in FIG. 4 a and the input alternatephase CPMG echo train preceding the primary phase (CPMG⁻¹) is shown inFIG. 4 c.

FIGS. 4 d and 4 e show the intermediate estimated ringing level resultsfrom Step 1 a: Ringing₊₁ in FIG. 4 d and Ringing⁻¹ in FIG. 4 c. Inaddition the intermediate estimated ringing level results are shown asthe horizontal lines in the respective plots: MeanRinging₊₁ in the upperplot and MeanRinging⁻¹ in the lower plot; with the magenta linerepresenting the real component and the cyan line representing theimaginary component.

FIG. 4 f shows the end of the ringing removal step for the currentprimary phase CPMG echo train where the final estimated ringing levels(MeanRingingAverage) from the Ringing Estimation step have been removedfrom the input primary phase CPMG echo train.

FIGS. 5 a-5 c show the effects of different levels of experimentstacking as would be applied in the Experiment Stacking step. For eachplot one track (in red color) shows the real channel and the other track(in green color) shows the imaginary channel.

FIG. 5 a is identical to FIG. 4 f, FIGS. 5 b and 5 c, respectively, showthat the method of this invention provides almost identical results asthe prior art method does when the same amount of experiment stacking(16 levels) is used.

FIGS. 5 d, 5 e and 5 f show how the signal-to-noise of the resultingCPMG echo trains improves with increased amounts of experiment stacking.

FIGS. 6 through 10 show how different amounts of experiment stackingimpact the vertical resolution of a section of log data. In particular,Track 1 shows a Density Porosity curve in black—computed from a BulkDensity log assuming grain and fluid densities of 2.65 and 1.0 gm/ccrespectively—the MRIL Effective porosity (MPHI) in magenta and MRIL BulkVolume Irreducible (MBVI) in red. Track 2 shows the T2 distributionresulting from the MAP inversion algorithm.

The illustrative examples show that vertical resolution improves as thelevel of experiment stacking decreases with a corresponding trade-off ofreduced accuracy of the inversion results. The accuracy reduction can beacceptable to a point the user is comfortable with, which then sets theacceptable vertical resolution for any particular data set.

D. Alternatives to Box-Car Filtering

Described below are approaches for improving the vertical resolution ofNMR logs by replacing the box-car filter used in the prior art forremoving both coherent and random noise signals, with a combination oftwo filters, in which the above functions are advantageously separated.A particular problem addressed below is that since in multi-frequencytools any two PAPs are separated by N CPMG pulse sequences, where N isthe number of operating frequencies, the filter length used in the priorart has to be a multiple of 2*N. Due to this limitation, very longfilters have to be used in the prior art, especially when the number Nof operating frequencies is high. For example, there are N=8 operatingfrequencies that can be used in a MRIL tool, so if full use is made ofthese frequencies, the minimum filter length is 16. Due to relativelylow signal levels and the corresponding need for signal stacking, filterlengths of 64 are not uncommon.

D.1. Prior Art Filtering

The current processing practice involves the use of boxcar (BC) filters,which simultaneously perform phase alternated pair (PAP) stacking forcoherent noise removal, and signal averaging for random noise reduction.The filter lengths used to this end are referred to as the RunningAverage (RA), and are multiples of the so called Minimum Running Average(MRA). As known in the art, the MRA depends on the type of the tool andits activation (i.e., dithered vs. non-dithered). The minimum filterlengths for the BC filters, for both MRIL-C and MRIL-Prime tools areshown in the following Table 1.

TABLE 1 Minimum Running Averages (MRA) for MRIL-C, and MRIL-Prime ToolsTool No. of Freq. Dithering MRA MRIL-C 2 No 4 MRIL-C 2 Yes 8 MRIL-Prime8 No 16

In general, the filter length, or running average RA, is determined byσ_(n), which is the standard deviation of the noise. The proper runningaverage filter length is defined as RA=n·MRA that results in σ_(n)=1,where n is an integer number. Although BC filters are efficient,primarily because of the simultaneous treatment of coherent and randomnoise components, and are easy to implement, there are four generalproblems associated with their use in practical applications.

First, in most high-gain environments (oil based mud, 8.5-inch hole,high frequency operation, etc.), the RA that results in σ_(n)≈1 can beas low as 4. However, the actual running average used in such cases istypically larger due to the MRA condition. For example, consider ahigh-gain case, where RA=4 would be sufficient. The actual runningaverage to be used, however, has to be 16 for the MRIL-Prime tool, or 8for a dual-frequency MRIL-C tool (4 if the activation is not dithered).

Next, the constraint that the RA must be a multiple of MRA, results in asimilar problem, particularly for tools such as the MRIL Prime tool. Forexample, consider the case of a MRIL Prime measurement, where RA=24would actually satisfy the σ_(n)≈1 condition. Since MRA is 16 for theMRIL Prime tool, an RA value of 36 must be used instead of 24.

Further, the boxcar filter has an equal-weight distribution, whichcauses significant degradation of vertical resolution in those caseswhere a large number of CPMGs must be stacked for proper random noisecancellation. Consider, for example, a very highly conductive mud, whereRA=48, and the sampling rate is 2 CPMGs per foot. In this case, a singlepoint on the porosity log represents a formation volume thickness of 24feet, and a bed near the edge of the sampled volume has equal weight inthe porosity as a bed just at the mid-point.

Finally, the output of the boxcar filter is generally very noisy. Thefrequency response of several boxcar filters can be seen in FIG. 12.Notable in the figure is the presence of many notches in the frequencyresponse, as well as the numerous secondary peaks. In practicalapplications these notches, in addition to the secondary peaks, causeoscillatory and noisy behavior. Further, one can note the secondarypeaks, marked in FIG. 12 as p1 to p6. These peaks generate noise, sincethey are at or above −20 db level, which is considered the detectionthreshold for human eye.

D.2. An Alternative Approach

In accordance with the present invention an alternative approach isproposed that eliminates problems associated with the prior art. It isperceived that the main problem with the BC filter (in addition to itsnoisy behavior for large N) is its equal-weight distribution; as notedabove, depending on the length of the filter local features may be lost.In accordance with the present invention it is proposed to use a taperedfilter, such as the Hamming filter, which generally results in betterpreservation of the local features. Unfortunately, however a taperedfilter alone cannot deal with the coherent noise components, due to thevery nature of the MRIL data acquisition in multi-frequency mode. Thus,in accordance with the present invention removal of the coherentnon-formation signals must be performed prior to the application of atapered filter. The prior art discloses the use of PAPs to this end. Thedisclosure in Sections II.A/B and C this application illustrate otherways of removing this undesirable signal component.

In contrast to the simultaneous treatment of coherent and random noiseby the boxcar approach, use of a tapered filter requires a two stepapproach, where PAPs-type processing to remove coherent noise signalcomponents is followed by a tapered filter, as explained below.

First, a Comb filter of length n (Cn) is applied to perform removal ofthe coherent noise components. A plot of the box-car and a Comb filter,for N=7, can be seen in FIGS. 13A and 13B. The filter lengths for theComb filter depend on the tool and its activation type, and are listedin Table 2 below. Note that in this approach each CPMG sequence thatbelongs to a particular frequency is combined with its true phasealternated pair. CPMGs from other frequencies are not involved in thisoperation.

TABLE 2 Comb filter lengths for MRIL-C, and MRIL-Prime Tools Tool No. ofFreq. Dithering Length (n) MRIL-C 2 No 3 MRIL-C 2 Yes 5 MRIL-Prime 8 No9

Secondly, a tapered filter of length n, such as a Hamming filter (HMn),is applied to the already phase alternated CPMGs, as shown in theillustrative examples below. This operation preserves more of the localinformation, while reducing random noise. A Hamming filter isillustrated in FIG. 13C.

While the definitions of these filters are well known in the art, theyare repeated next for convenience.

For all the filter definitions given below, N is the number of thefilter elements, where it is assumed that they run between 1≦i≦N.Information on other tapered filters can be found in standard signalprocessing references, such as “Handbook for Digital Signal Processing”,Edited by Sanjit Mitra and James Kaiser, Wiley & Sons, Inc. 1993. Thecontent of this reference relevant to filter design is herebyincorporated by reference for background.

-   1. BCn. BoxCar filter with N points. The filter coefficients are    given by $f_{i} = \frac{1}{N}$-   2. Cn. Comb filter with N points. The filter coefficients are given    by $\begin{matrix}    {f_{i} = 0.5} & {{{for}\quad i} = {{1\quad{and}\quad i} = N}} \\    {\quad 0.0} & {{otherwise}\quad}    \end{matrix}$-   3. HMn. Hamming filter with N points. The filter coefficients are    given by    $f_{i} = {0.54 - {0.46\quad{\cos\left\lbrack \frac{2\quad{\pi\left( {i - 1} \right)}}{N - 1} \right\rbrack}}}$

The overall effect of the Comb filter and the tapered filter can beanalyzed by considering the Fourier transform of their convolution.Comparison of the current and proposed methodologies based on theirFourier transforms is illustrated below. It should be noted that Filter1 and Filter 2 in accordance with this invention need not necessarily beseparate and distinct entities—in specific implementations they could bebuilt into a single filter that has the response corresponding to theconvolution of the two separate filters. For reasons of conceptualsimplicity, the two filters are considered as being separate in thesequel.

Filter Response Comparison

Assume a hypothetical case where 16 CPMGs must be stacked to satisfy theσ_(n)≈1 condition. The response of the proposed approach in accordancewith the present invention is compared to the response of theconventional boxcar filter in three separate cases simulating:

-   -   1. Dual-frequency MRIL-C, non-dithered activation (C3HM16),    -   2. Dual-frequency MRIL-C, dithered activation (C5HM16),    -   3. MRIL-Prime (C9HM16).        Case 1: BC16 vs. C3HM16

In the case of a dual-frequency MRIL-C tool, with a non-ditheredactivation, a Ccomb filter of length 3 is followed by a Hamming filterof length 16. The comparison of BC16 vs. C3HM16 is given in FIG. 14. Asshown, the BC16 filter has a notch at k=0.125, and two peaks at k=0.175,and k=0.32, all generating noise in a visible range. The C3HM16 filteron the other hand monotonically decreases, has no significant notches,or secondary visible peaks. There is a significant improvement in thevertical resolution, with almost no side-lobe noise.

Case 2: BC16 vs. C5HM16

In the case of a dual-frequency MRIL-C tool with dithered activation, acomb filter of length 5 is followed by a Hamming filter of length 16.The comparison of BC16 vs. C5HM16 is given in FIG. 15. The C5 HM16filter decreases monotonically, as in FIG. 14. Although the boxcarfilter may appear to contain a larger proportion of the wavelengthsaround k=0.18, the notch followed by a peak causes oscillations in thelogs. The first notch of the C5HM16 filter occurs at a laterspatial-frequency, improving vertical resolution, and the followingside-lobe is much smaller compared to the boxcar filter, resulting insignificantly reduced side-lobe noise.

Case 3: BC16 vs. C9HM16

In the case of an MRIL-Prime tool, a comb filter of length 9 is appliedbefore a Hamming filter of length 16. The comparison of BC16 vs. C9HM16is given in FIG. 16. Both filters have similar responses up to the firstnotch, explaining why the proposed method may not improve verticalresolution in this particular instance. However, the C9HM16 filtergenerates a less-noisy response (by approximately 6 dB), since its mainside-lobe is weaker compared to the BC16 filter. The second peak of theC9HM16 filter is not as strong as that of the BC16. Although this mayimply better resolution on the part of the BC16 filter, the strongersecond peak is actually a source of noise that can be observed on thelogs. The more suppressed second peak of the C9HM16 response results ina cleaner response.

Filter Response Comparison for Longer Filter Lengths

Filter responses for BC32 and BC64, vs. C9HM32 and C9HM64, respectively,can be seen in FIGS. 17 and 18. As the RA gets larger, the locations ofthe first notch in both filters converge. However, the secondary peak inthe C9HM32 or C9HM64 filters is much weaker, resulting in cleaner logresponse. As illustrated in FIG. 17 for a comparison of BC32 and C9HM32filters, the notch in the CM9HM32 filter occurs at a higherspatial-frequency, thereby increasing the inherent vertical resolution.Also note the weaker side-lobe (compared to C9HM32), after the firstnotch.

FIG. 18 illustrates a comparison of the BC64 and C9HM64 filters. Theinherent vertical resolution of the C9HM64 filter clearly is better,since the first notch occurs at a higher spatial-frequency compared tothe BC64 filter.

Log Examples

Non-dithered MRIL-C Log

The four filters, BC16, C3HM16, C5HM16, and C9HM16 were applied to a1995-vintage, dual-frequency MRIL-C log. The activation used at the timewas not dithered. The results of the four filters can be seen in FIG.19. The logs have been offset by a constant amount to allow easiervisual identification of the features. Porosity from the conventionalBC16 process is the red curve, easily identified by jittery noise. Theblack curve corresponds to the C3HM16 filter, which has the bestvertical resolution and the most stable appearance. The other twocurves, corresponding to C5HM16 (shown in dotted line) and C9HM16filters, are also better than the BC16 case, but not as good as theC3HM16 filter. Note the excellent agreement between the theory and theresults.

MRIL-C Log, BA Test Well, 6 Second Wait Time

A comparison of standard processing, vs. the method of this invention,in a Baker-Atlas well are shown in FIGS. 20 and 21. Log A is standardMRIL boxcar processing, with a post-inversion cosine filter applied,while B is the same log without the cosine filter. Log C shows resultsfrom the new method, with clear improvements in vertical resolution.FIG. 20 is a Baker-Atlas Test Well, MRIL-C log, 6 second wait time. FIG.20(A) illustrates standard MRIL boxcar processing with post-inversioncosine filter; FIG. 20(B) is the same as (A), without the cosine filter;and FIG. 20(C) illustrates the new method. While porosities in FIG. 20(A) and (B) contain contributions from the PR06 data set, the porositylog in (C) has been obtained only from the t_(e)=1.2 ms data set.

MRIL-C Log, BA Test Well, 3 Second Wait Time

A comparison of the logs, in the same well, but with a wait time of 3seconds is shown in FIG. 21. FIG. 21(A) is the standard processing, FIG.21(B) illustrates the new method. As in the previous figure, theporosity curve in (B) has been obtained from the 1.2 ms data set only.The logging speeds in FIGS. 20 and 21 are close, such that the reductionin the wait time, when using similar stacking levels, results inimproved vertical resolution, independent of the method. The zone shownin FIG. 21 covers the same sand in the previous figure, and anothershorter zone above it.

Based on the above examples, the following observations can be made: analternative pre-processing method has been developed to improve thevertical resolution of NMR logs. The methods proposed in Section Dreplace the boxcar filter with the combination of a comb filter, and atapered filter, and is equally applicable to a variety ofmulti-frequency tools.

Next, overall the filter response of the method of this invention isless noisy than the boxcar filter. The side-lobes in the filters (afterthe first notch) are alternately anti-phase and in-phase with themain-lobe. Consequently, the first side-lobe contributes a strong signalout of phase with the true signal. Hence, a strong first side-lobe willgenerate appreciable noise (as in the case of boxcar filters), whileweaker side-lobes (as in the case of the proposed method) will result inmuch cleaner response. Indeed, it appears likely that noise originatingfrom the first side-lobe of the boxcar filter is what necessitates theadditional application of a cosine filter in the post-inversion phase ofthe current processing.

In low SNR conditions, where RA>>MRA, the proposed method cansignificantly enhance the vertical resolution of both the MRIL-C andMRIL-D tools, while significantly reducing filter side-lobe noise.

In high SNR conditions (such as oil-based mud, high frequency operation,etc.), the proposed method can significantly enhance the verticalresolution of MRIL-C logs. The improvements are more dramatic in thecase of non-dithered activations.

Although a Hamming filter has been used in a specific embodimentillustrated in the drawings, a large selection of filters exists inliterature, which can be used in alternate embodiments, dependent on theparticular application and ease of implementation.

D.3 Implementation Issues

FIGS. 22, 23 and 24 illustrate in more detail the implementation of themethod of the present invention discussed in Section D of thedisclosure. More specifically, FIG. 22 illustrates in a flow-diagramform the use of two filters to replace the single boxcar filter employedby the prior art.

As illustrated in FIG. 22, the first step 1 is of acquisition & storageof a depth-varying sequence of multi-frequency PAP echo trains, whichare designated in the figure for purposes of illustration as echo trains“a”. In the following step 2 of the method the multi-frequencyecho-trains input signal is separated into multiple data-flow paths, onepath per frequency, resulting in N data flow paths, corresponding to theoperating frequencies f1-fN of the tool.

In the following step 3 of the processing algorithm, Filter 1 is appliedseparately to the data “b” in each data-flow path, producing as theoutput from each path a sequence of “clean” echo-trains “c” referencedto the mid-point of each echo-train PAP. In the context of thisapplication “clean” denotes that the echo trains no longer contain thenon-formation signals that the PAP method or the methods discussed inSections A, B and C of this application are designed to remove.

In the following step 4 of the method, the separate data-flow paths arere-combined into a single data-flow of the clean echo trains; in thefollowing step 5, Filter 2, as discussed above, is applied to thesequence of clean echo-trains in this recombined data-flow path.

Finally, in step 6, subsequent processing of the clean echo-trains “d”using standard procedures, such as MAP inversion, is applied as known inthe art.

With reference to FIG. 23, an alternative embodiment of the presentinvention can be used, where the processing modification would allow theuser to obtain, for example, the best possible inversions at multipledepths of investigation (lower frequency =>deeper investigation per MRILdesign). In particular, and with further reference to the discussionconcerning FIG. 22, step 4 of re-combining the data paths is eliminated,so that after “cleaning” echo trains b of frequencies f1-fN using Filter1 in step 3, a separate filter is applied to echo trains c in each datapath, as shown in FIG. 23A. In accordance with this embodiment furtherillustrated in FIG. 23B, a Filter 2′ (designed in the same manner asFilter 2 discussed above) is applied in step 5′ to obtain optimumvertical resolution for a given SNR—even though the data is much sparserthan with the recombined echo-trains—and to produce multiplefrequency-separated clean echo trains “e” with optimum verticalresolution for the required SNR. Subsequent processing of thefrequency-separated clean echo-trains using standard procedures isapplied in step 6′, as known in the art.

With reference to FIGS. 24A and 24B, in an alternative embodiment, thefiltering in Step (3) could be replaced by (3′) the data-drivendetermination of the ringing signal in data-flow paths for frequenciesf1-fN with subsequent removal from the echo-trains. Data drivendetermination of the ringing signal is discussed in more detail inSection A of this application. [RE&E—Ringing Estimation & Elimination].Subsequent processing can be either by combining output signals from alldata path and applying Filter 2 (not shown), as described previouslywith reference to FIG. 22, or by applying Filter 2′ (not shown) to eachdata path, as described previously with reference to FIG. 23, or withother methods not explicitly described.

E. Overall System and Method Considerations

In accordance with the present invention, and as also indicated above,the methods disclosed in Sections A, B, C and D can be usedadvantageously in combination. It is noted first that the method inSection D, can be used to replace boxcar filtering in all practicalapplications. In the more special case when the SNR of the formationdata is sufficiently high, it can be supplemented with processing of thetype discussed in Sections A-C.

More specifically, in a preferred embodiment a NMR system for datalogging and analysis is operated as follows. First, the method disclosedin Section D is initially applied and used to estimate the SNR, which isobtained from the input data. Next is determined if thevertical-resolution is sub-optimal and, if so, the processing isswitched to the ringing estimation method discussed in Sections A-C.

In an alternative embodiment, one can start by using the Direct RingingEstimation approach discussed in Section A.1.b; based on the resultsfrom this step one can then estimate what filter length is needed toobtain adequate SNR. If the estimated filter length is consistent withthe approach discussed in Section D, the operation is switched for thisprocessing.

In general, it will be noted that the filtering approach disclosed inSection D is likely to be more robust, as it does not make anyassumptions about the ringing signal other than that it is essentiallyunchanged between any two echo-trains that make up a PAP. The estimationof ringing, on the other hand, makes some assumptions about the ringingsignal, which in the preferred embodiment is quite simple, i.e., thatthe ringing signal is characterized by an offset (in the complex space)to the real and imaginary components in the NMR signal, which remainessentially unchanged between any two echo-trains that make up a PAP.

The combination discussed above is believed to be a significantcontribution to the art of NMR logging with wide ranging applicationsinvolving virtually all NMR tools, and a broad range of practicalapplications, including logging while drilling.

While the invention has been described with reference to the preferredembodiments, it will be appreciated by those of ordinary skill in theart that modifications can be made to the structure and form of theinvention without departing from its spirit and scope which is definedin the following claims.

1. A method for increasing the resolution of NMR log data obtained usinga multi-frequency NMR tool having N (N≧2) operating frequencies,comprising: (a) providing an NMR pulse echo signal having componentscorresponding to at least two operating frequencies of the tool; (b)separating the provided pulse echo signal into two or more data-flowpaths, each data flow path corresponding to an operating frequency ofthe tool; (c) removing coherent noise components from the signals inseparate data flow paths; and (d) combining output signals from theseparate data flow paths to remove random noise components.
 2. Themethod of claim 1, wherein in step (c) signals in each data flow pathare filtered to reduce the contribution of non-formation signalcomponents.
 3. The method of claim 1, wherein in step (d) output signalsfrom the separate data flow paths are filtered to achieve apredetermined signal-to-noise ratio (SNR) for a given resolution of theNMR log data.
 4. The method of claim 3, wherein the filtering in step(d) is performed using a tapered filter.
 5. The method of claim 4,wherein the tapered filter is a Hamming filter.
 6. The method of claim1, wherein the number of operating frequencies of the tool is N=8. 7.The method of claim 1, wherein the removing operation in step (c) isperformed on phase alternated pairs (PAPs) of signals.
 8. The method ofclaim 7, wherein the removing operation in step (c) comprisessubtracting on an element-by-element basis NMR spin echo signalscorresponding to said PAPs.
 9. The method of claim 1, wherein outputsignals from the separate data flow paths in step (c) are combined inone re-combined signal.
 10. A system for increasing the resolution ofNMR log data obtained using a multi-frequency NMR tool having Noperating frequencies, comprising: means for providing a NMR pulse echosignal comprising components corresponding to at least two operatingfrequencies of the tool; means for separating the provided pulse echosignal into two or more data-flow paths, each data flow pathcorresponding to an operating frequency of the tool; means for removingcoherent noise components from the signals in separate data flow paths;and means for combining output signals from the separate data flow pathsto remove random noise components.
 11. The system of claim 10 furthercomprising means for filtering signals in each data flow path to reducethe contribution of non-formation signal components.
 12. The system ofclaim 10, wherein said means for combining comprises filtering meansdesigned to achieve a predetermined signal-to-noise ratio (SNR) for agiven resolution of the NMR log data.
 13. The system of claim 11,wherein the filtering means comprises a tapered filter.
 14. The systemof claim 13, wherein the tapered filter is a Hamming filter.
 15. Amethod for increasing the resolution of NMR log data obtained using amulti-frequency NMR tool having N (N≧2) operating frequencies,comprising: (a) providing an NMR pulse echo signal having componentscorresponding to at least two operating frequencies of the tool; (b)separating the provided pulse echo signal into two or more data-flowpaths, each data flow path corresponding to an operating frequency ofthe tool; (c) filtering the signal in each data flow path using a firstfilter designed to reduce the contribution of coherent noise components;and (d) filtering the output signal from the first filter to achieve apredetermined signal-to-noise ratio (SNR) for a given resolution of theNMR log data.
 16. The method of claim 15, wherein N=8.
 17. The method ofclaim 15, wherein the filtering operation in step (c) is performed onphase alternated pairs (PAPs) of signals.
 18. The method of claim 17,wherein the filtering operation in step (c) comprises subtracting on anelement-by-element basis NMR spin echo signals corresponding to saidPAPs.